(1/2x+12)+(7x+5)=180

Solution for (1/2x+12)+(7x+5)=180 equation:

(1/2x+12)+(7x+5)=180

We move all terms to the left:

(1/2x+12)+(7x+5)-(180)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

1/2x+7x+12+5-180=0

We multiply all the terms by the denominator


7x*2x+12*2x+5*2x-180*2x+1=0

Wy multiply elements

14x^2+24x+10x-360x+1=0

We add all the numbers together, and all the variables

14x^2-326x+1=0

a = 14; b = -326; c = +1;
Δ = b2-4ac
Δ = -3262-4·14·1
Δ = 106220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{106220}=\sqrt{4*26555}=\sqrt{4}*\sqrt{26555}=2\sqrt{26555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-326)-2\sqrt{26555}}{2*14}=\frac{326-2\sqrt{26555}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-326)+2\sqrt{26555}}{2*14}=\frac{326+2\sqrt{26555}}{28}
$